Development of a knowledge based program to design epicyclic gear trains

Abstract

A number of studies are devoted to the systematic synthesis of the structure of mechanisms. the basic idea of the synthesis is to separate the structure of a mechanism from is function. The kinematic structure of a type of mechanisms, i.e., an equivalent class of mechanisms having the same degree of freedom, number of elements, and nature of desired functions, has been enumerated systematically using a graph theory. And then, the results of enumeration are classified and partitioned according to user specified functions of mechanisms. Implemented on a computer, this scheme can bring out better quality mechanisms in less time even by a less-experienced designer. In this work, a method of identifying nonisomorphic graphs is introduced with the aid of graph enumeration theory. Edge permutations which are induced from the symmetric group of vertex permutations are used as mapping functions to identify nonisomorphic graphs among those with given number of vertices. This method is applied to the enumeration of nonisomorphic graphs and the result is used for the synthesis of one-degree-of-freedom epicyclic gear trains. The entire procedure of enumeration is programmed in LISP. The result of the enumeration of graphs with up to 7 elements is presented. It is shown that there are 144 nonisomorphic rotation graphs and 642 nonisomorphic labeled graphs from which all the 7-link epicyclic gear trains can be derived. A program for design of power transmissions using epicyclic gear trains is developed as a knowledge based system. The result of enumeration is used as data from which one or a set of mechanisms satisfying user prescribed functions is selected. One of the main functions of power transmissions is to obtain various output speeds for a constant input. As the first stop of design procedure, a designer is required to enter the number of speed ratios and the option whether a reverse or an over-drive stage is to be included in the design. Secondly a set of rules for g...